Details

analyze29.0ms (0.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	49.7%	50.3%	0
0%	49.7%	50.3%	1
0%	49.7%	50.3%	2
24.8%	24.8%	50.3%	3
37.3%	12.4%	50.3%	4
43.5%	6.2%	50.3%	5
46.6%	3.1%	50.3%	6
48.1%	1.6%	50.3%	7
48.9%	0.8%	50.3%	8
49.3%	0.4%	50.3%	9
49.5%	0.2%	50.3%	10
49.6%	0.1%	50.3%	11
49.6%	0%	50.3%	12
49.7%	0%	50.3%	13
49.7%	0%	50.3%	14

Compiler

Compiled 16 to 12 computations (25% saved)

sample202.0ms (1.9%)

Algorithm

1×

intervals

Results

152.0ms	111×	body	2048	valid
22.0ms	70×	body	1024	valid
7.0ms	39×	body	512	valid
4.0ms	256×	pre	128	true
3.0ms	5×	body	4096	valid
2.0ms	20×	body	256	valid
1.0ms	11×	body	128	valid

Compiler

Compiled 26 to 20 computations (23.1% saved)

simplify15.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

39×	`fma-def_binary64`
32×	`fma-neg_binary64`
14×	`cancel-sign-sub-inv_binary64`
12×	`sub-neg_binary64`
10×	`distribute-rgt-in_binary64`

Counts

1 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	12
1	11	12
2	17	12
3	25	12
4	33	12
5	51	12
6	76	12
7	93	12
8	110	12
9	120	12
10	124	12
11	126	12
12	112	12

prune1.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Kept	Total
New	0	0
Fresh	1	1
Picked	0	0
Done	0	0
Total	1	1

Error

59.6b

Counts

1 → 1

Alt Table

Status	Error	Program
▶	59.6b	(-.f64 (/.f64 1 x) (/.f64 1 (tan.f64 x)))

Compiler

Compiled 18 to 14 computations (22.2% saved)

localize5.0ms (0%)

Local error

Found 1 expressions with local error:

4.3b	(-.f64 (/.f64 1 x) (/.f64 1 (tan.f64 x)))

rewrite260.0ms (2.4%)

Algorithm

1×	rewrite-expression-head

Error

58.8b

Rules

279×	`times-frac_binary64`
230×	`add-sqr-sqrt_binary64`
222×	`*-un-lft-identity_binary64`
206×	`add-cube-cbrt_binary64`
182×	`prod-diff_binary64`

Counts

1 → 239

Calls

1 calls:

18.0ms

(-.f64 (/.f64 1 x) (/.f64 1 (tan.f64 x)))

Compiler

Compiled 9003 to 5624 computations (37.5% saved)

series19.0ms (0.2%)

Error

0.3b

Counts

1 → 7

Calls

1 calls:

14.0ms

(-.f64 (/.f64 1 x) (/.f64 1 (tan.f64 x)))

Compiler

Compiled 152 to 112 computations (26.3% saved)

simplify283.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

387×	`fma-neg_binary64`
381×	`fma-def_binary64`
371×	`unsub-neg_binary64`
338×	`distribute-rgt-in_binary64`
281×	`associate-l_binary64`

Counts

246 → 241

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	146	8476
1	305	4719
2	752	3262
3	2307	3262
4	4031	3262
5	4728	3262
6	4999	3262
7	4794	3262

prune20.0ms (0.2%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	240	1	241
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	241	1	242

Error

0.3b

Counts

242 → 1

Alt Table

Status	Error	Program
▶	0.3b	(fma.f64 2/945 (pow.f64 x 5) (fma.f64 1/3 x (*.f64 1/45 (pow.f64 x 3))))

Compiler

Compiled 571 to 379 computations (33.6% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.1b	(*.f64 1/45 (pow.f64 x 3))
0.3b	(fma.f64 1/3 x (*.f64 1/45 (pow.f64 x 3)))

rewrite44.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Error

0.3b

Rules

13×	`add-sqr-sqrt_binary64`
12×	`associate-r_binary64`
7×	`add-exp-log_binary64`
6×	`*-un-lft-identity_binary64`
6×	`add-cube-cbrt_binary64`

Counts

2 → 43

Calls

2 calls:

5.0ms	(*.f64 1/45 (pow.f64 x 3))
1.0ms	(fma.f64 1/3 x (*.f64 1/45 (pow.f64 x 3)))

Compiler

Compiled 706 to 558 computations (21% saved)

series20.0ms (0.2%)

Error

0.3b

Counts

2 → 9

Calls

2 calls:

10.0ms	(fma.f64 1/3 x (*.f64 1/45 (pow.f64 x 3)))
6.0ms	(*.f64 1/45 (pow.f64 x 3))

Compiler

Compiled 265 to 210 computations (20.8% saved)

simplify108.0ms (1%)

Algorithm

1×	egg-herbie

Rules

541×	`associate-l_binary64`
505×	`associate-r_binary64`
426×	`log-prod_binary64`
346×	`exp-prod_binary64`
345×	`swap-sqr_binary64`

Counts

52 → 27

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	72	586
1	125	523
2	339	523
3	1827	523
4	3512	493
5	4560	493
6	4941	493
7	4973	493

prune12.0ms (0.1%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	26	1	27
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	26	2	28

Error

0.3b

Counts

28 → 2

Alt Table

Status	Error	Program
▶	36.4b	(fma.f64 2/945 (pow.f64 x 5) (cbrt.f64 (pow.f64 (fma.f64 1/3 x (*.f64 1/45 (pow.f64 x 3))) 3)))
✓	0.3b	(fma.f64 2/945 (pow.f64 x 5) (fma.f64 1/3 x (*.f64 1/45 (pow.f64 x 3))))

Compiler

Compiled 290 to 223 computations (23.1% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(*.f64 1/45 (pow.f64 x 3))
0.2b	(pow.f64 (fma.f64 1/3 x (*.f64 1/45 (pow.f64 x 3))) 3)
0.3b	(fma.f64 1/3 x (*.f64 1/45 (pow.f64 x 3)))
36.4b	(cbrt.f64 (pow.f64 (fma.f64 1/3 x (*.f64 1/45 (pow.f64 x 3))) 3))

rewrite112.0ms (1%)

Algorithm

1×	rewrite-expression-head

Error

0.3b

Rules

21×	`add-sqr-sqrt_binary64`
14×	`*-un-lft-identity_binary64`
14×	`add-cube-cbrt_binary64`
12×	`associate-r_binary64`
12×	`cbrt-prod_binary64`

Counts

4 → 91

Calls

4 calls:

5.0ms	(*.f64 1/45 (pow.f64 x 3))
3.0ms	(pow.f64 (fma.f64 1/3 x (*.f64 1/45 (pow.f64 x 3))) 3)
2.0ms	(cbrt.f64 (pow.f64 (fma.f64 1/3 x (*.f64 1/45 (pow.f64 x 3))) 3))
0.0ms	(fma.f64 1/3 x (*.f64 1/45 (pow.f64 x 3)))

Compiler

Compiled 1787 to 1471 computations (17.7% saved)

series99.0ms (0.9%)

Error

0.3b

Counts

4 → 26

Calls

4 calls:

25.0ms	(pow.f64 (fma.f64 1/3 x (*.f64 1/45 (pow.f64 x 3))) 3)
23.0ms	(fma.f64 1/3 x (*.f64 1/45 (pow.f64 x 3)))
17.0ms	(cbrt.f64 (pow.f64 (fma.f64 1/3 x (*.f64 1/45 (pow.f64 x 3))) 3))
11.0ms	(*.f64 1/45 (pow.f64 x 3))

Compiler

Compiled 875 to 721 computations (17.6% saved)

simplify141.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

723×	`distribute-rgt-in_binary64`
714×	`distribute-lft-in_binary64`
379×	`fma-def_binary64`
224×	`*-commutative_binary64`
220×	`unswap-sqr_binary64`

Counts

117 → 76

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	130	1746
1	240	1573
2	682	1545
3	1623	1545
4	4964	1545

prune64.0ms (0.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	73	3	76
Fresh	0	0	0
Picked	1	0	1
Done	0	1	1
Total	74	4	78

Error

0.3b

Counts

78 → 4

Alt Table

Status	Error	Program
	52.1b	(fma.f64 2/945 (pow.f64 x 5) (cbrt.f64 (cbrt.f64 (pow.f64 (pow.f64 (fma.f64 1/3 x (*.f64 1/45 (pow.f64 x 3))) 3) 3))))
▶	25.4b	(fma.f64 2/945 (pow.f64 x 5) (.f64 (cbrt.f64 (pow.f64 (fma.f64 1/3 x (.f64 1/45 (pow.f64 x 3))) 2)) (cbrt.f64 (fma.f64 1/3 x (*.f64 1/45 (pow.f64 x 3))))))
	36.5b	(fma.f64 2/945 (pow.f64 x 5) (cbrt.f64 (fma.f64 (pow.f64 x 3) 1/27 (*.f64 1/135 (pow.f64 x 5)))))
✓	0.3b	(fma.f64 2/945 (pow.f64 x 5) (fma.f64 1/3 x (*.f64 1/45 (pow.f64 x 3))))

Compiler

Compiled 891 to 713 computations (20% saved)

localize26.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(fma.f64 1/3 x (*.f64 1/45 (pow.f64 x 3)))
0.3b	(fma.f64 1/3 x (*.f64 1/45 (pow.f64 x 3)))
0.7b	(cbrt.f64 (fma.f64 1/3 x (*.f64 1/45 (pow.f64 x 3))))
25.7b	(cbrt.f64 (pow.f64 (fma.f64 1/3 x (*.f64 1/45 (pow.f64 x 3))) 2))

rewrite124.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Error

0.2b

Rules

11×	`cbrt-prod_binary64`
7×	`*-un-lft-identity_binary64`
7×	`add-sqr-sqrt_binary64`
7×	`add-cube-cbrt_binary64`
4×	`add-cbrt-cube_binary64`

Counts

4 → 51

Calls

4 calls:

5.0ms	(cbrt.f64 (fma.f64 1/3 x (*.f64 1/45 (pow.f64 x 3))))
3.0ms	(cbrt.f64 (pow.f64 (fma.f64 1/3 x (*.f64 1/45 (pow.f64 x 3))) 2))
1.0ms	(fma.f64 1/3 x (*.f64 1/45 (pow.f64 x 3)))
1.0ms	(fma.f64 1/3 x (*.f64 1/45 (pow.f64 x 3)))

Compiler

Compiled 1703 to 1395 computations (18.1% saved)

series152.0ms (1.4%)

Error

0.3b

Counts

4 → 24

Calls

4 calls:

43.0ms	(cbrt.f64 (pow.f64 (fma.f64 1/3 x (*.f64 1/45 (pow.f64 x 3))) 2))
28.0ms	(cbrt.f64 (fma.f64 1/3 x (*.f64 1/45 (pow.f64 x 3))))
25.0ms	(fma.f64 1/3 x (*.f64 1/45 (pow.f64 x 3)))
22.0ms	(fma.f64 1/3 x (*.f64 1/45 (pow.f64 x 3)))

Compiler

Compiled 1963 to 1644 computations (16.3% saved)

simplify145.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

661×	`fma-def_binary64`
397×	`distribute-rgt-in_binary64`
333×	`fma-neg_binary64`
280×	`cancel-sign-sub-inv_binary64`
263×	`associate-l_binary64`

Counts

75 → 35

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	118	1440
1	248	1333
2	568	1227
3	2044	1143
4	4729	1142
5	4995	1142
6	4938	1142

prune30.0ms (0.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	32	3	35
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	33	6	39

Error

0.3b

Counts

39 → 6

Alt Table

Status	Error	Program
	52.1b	(fma.f64 2/945 (pow.f64 x 5) (cbrt.f64 (cbrt.f64 (pow.f64 (pow.f64 (fma.f64 1/3 x (*.f64 1/45 (pow.f64 x 3))) 3) 3))))
	36.5b	(fma.f64 2/945 (pow.f64 x 5) (cbrt.f64 (fma.f64 (pow.f64 x 3) 1/27 (*.f64 1/135 (pow.f64 x 5)))))
	25.5b	(fma.f64 2/945 (pow.f64 x 5) (.f64 (cbrt.f64 (pow.f64 (fma.f64 1/3 x (.f64 1/45 (pow.f64 x 3))) 2)) (.f64 (cbrt.f64 (cbrt.f64 (pow.f64 (fma.f64 1/3 x (.f64 1/45 (pow.f64 x 3))) 2))) (cbrt.f64 (cbrt.f64 (fma.f64 1/3 x (*.f64 1/45 (pow.f64 x 3))))))))
	25.6b	(fma.f64 2/945 (pow.f64 x 5) (.f64 (.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (fma.f64 1/3 x (.f64 1/45 (pow.f64 x 3)))) 4)) (cbrt.f64 (cbrt.f64 (pow.f64 (fma.f64 1/3 x (.f64 1/45 (pow.f64 x 3))) 2)))) (cbrt.f64 (fma.f64 1/3 x (*.f64 1/45 (pow.f64 x 3))))))
	25.9b	(fma.f64 2/945 (pow.f64 x 5) (.f64 (cbrt.f64 (.f64 1/9 (.f64 x x))) (cbrt.f64 (fma.f64 1/3 x (.f64 1/45 (pow.f64 x 3))))))
	0.3b	(fma.f64 2/945 (pow.f64 x 5) (fma.f64 1/3 x (*.f64 1/45 (pow.f64 x 3))))

Compiler

Compiled 853 to 683 computations (19.9% saved)

regimes441.0ms (4.2%)

Accuracy

Total 0.1b remaining (16.8%)

Threshold costs 0.1b (16.8%)

Compiler

Compiled 12156 to 8918 computations (26.6% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`
1×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	20
1	16	20
2	16	20

end1.0ms (0%)

Compiler: Compiled 15 to 12 computations (20% saved)

sample8.3s (77.7%)

Algorithm

1×

intervals

Results

6.3s	3981×	body	2048	valid
908.0ms	2000×	body	1024	valid
205.0ms	1046×	body	512	valid
156.0ms	8000×	pre	128	true
119.0ms	191×	body	4096	valid
65.0ms	540×	body	256	valid
15.0ms	242×	body	128	valid

Compiler

Compiled 187 to 152 computations (18.7% saved)

Iter	Nodes	Cost
0	7	12
1	11	12
2	17	12
3	25	12
4	33	12
5	51	12
6	76	12
7	93	12
8	110	12
9	120	12
10	124	12
11	126	12
12	112	12

Iter	Nodes	Cost
0	7	12
1	11	12
2	17	12
3	25	12
4	33	12
5	51	12
6	76	12
7	93	12
8	110	12
9	120	12
10	124	12
11	126	12
12	112	12

Details

analyze29.0ms (0.3%)

sample202.0ms (1.9%)

simplify15.0ms (0.1%)

prune1.0ms (0%)

localize5.0ms (0%)

rewrite260.0ms (2.4%)

series19.0ms (0.2%)

simplify283.0ms (2.7%)

prune20.0ms (0.2%)

localize7.0ms (0.1%)

rewrite44.0ms (0.4%)

series20.0ms (0.2%)

simplify108.0ms (1%)

prune12.0ms (0.1%)

localize10.0ms (0.1%)

rewrite112.0ms (1%)

series99.0ms (0.9%)

simplify141.0ms (1.3%)

prune64.0ms (0.6%)

localize26.0ms (0.2%)

rewrite124.0ms (1.2%)

series152.0ms (1.4%)

simplify145.0ms (1.4%)

prune30.0ms (0.3%)

regimes441.0ms (4.2%)

simplify3.0ms (0%)

end1.0ms (0%)

sample8.3s (77.7%)

Profiling

Iter	Nodes	Cost
0	7	12
1	11	12
2	17	12
3	25	12
4	33	12
5	51	12
6	76	12
7	93	12
8	110	12
9	120	12
10	124	12
11	126	12
12	112	12